Are military style ( tan color, Mille straps, etc) ok to use while touring France and England?
You mean as your main luggage or a day bag?
As a day bag it may be larger than museums etc permit and may require it be checked.
Sure. There are plenty of French and English military and ex-military people out and about, and surplus gear sold everywhere. I wouldn't hang anything suspicious on the molle straps, however.
Shouldn't be an issue.
Keep the morale patches to a minimum.
Just make sure you comply with weight and dimensions allowed by the airlines and museums.
Just bear in mind - the more pockets your pack has, the longer you will spend in security while they search them all.
My thought was essentially the same as Simon's. When you visit a museum, you get in much faster carrying nothing. If you can't live with nothing, a very small bag with only one opening is nearly as fast. Some places will let you in with a bag after it's inspected, many others require you to check your bag or stow it in a locker.
I have photos of myself alone with the Mona Lisa at the Louvre. I had intended to skip it because I prefer avoiding crowds. I was in line early, museum pass in hand and no bags. I was first in the pass line and was waived through security so found myself literally the only patron in the Louvre for maybe five minutes. The next couple had pre-purchased tickets online but carried several bags. The first people who needed to get tickets were at least ten minutes behind. I made a bee-line for the Mona Lisa and arrived well before any crowd could form. When the couple caught up, we traded taking photos of each other.